This quest is there in case Hawke has spent too much to be able to finance the expedition after having done all the other quests. If you accept, the money will be sent to Bartrand so that you can continue the plot. When you return he will confront you at the Hawke Estate, asking for an additional 100 gold. You then have the choice of either paying up or refusing; refusing will result in fighting him at a later point in the game.

The player can earn around 100 gold during Act 1 (without using increased gold drop equipment, etc.); unless spending money recklessly, it is very unlikely the player needs to accept Dougal's offer. ( Confirmed for v1.04 Normal Difficulty, with all main, side, secondary and companion quests done, a diplomatic Hawke could amass 115 gold in Act 1 without spending any )

If you have Varric in your party when talking to Dougal, Varric will interject with a few lines of dialogue here and there which gives you a better idea of the bitter relationship between Dougal and Bartrand. There's a dialogue option where you can directly ask Varric what he thinks, but it won't result in gaining any friendship with him.

This quest also appears if you already have enough money for the expedition. If you've already given the 50 gold to Bartrand, this quest will automatically be completed if accepted.

If you earn the coin yourself and skip or refuse this quest, at the end of the Deep Roads Expedition you will be rewarded by getting your 50 gold back as your "earnings from the expedition".